This report presents a reproducible numerical investigation of boundary-layer structures in a degenerate mixed-gradient dissipative field model developed within the Boundary Information Geometry (BIG) framework. The study examines stationary solutions of ∂tφ = ∇·(φ²∇φ) − μφ − γ∇·(|∇φ|²∇φ) + S(x), with fixed quartic-gradient stiffness γ = 1 and varying dissipation parameter μ. A shell-based local asymptotic fitting procedure is used to analyze free-boundary behavior. The local boundary profile is fitted by φ(s) ~ A s^ν, allowing extraction of the boundary exponent ν together with layer-quality diagnostics. Three numerical stages were performed: • Reproducibility audit• Extended μ scan• Collapse-region investigation The principal observation is the persistence of a quadratic boundary exponent ν ≈ 2 throughout the interval 0.1 ≤ μ ≤ 1.1. While the exponent remains remarkably stable, the coherent quadratic-layer width decreases as dissipation increases. Near μ ≈ 1, coherent quadratic layers disappear according to amplitude-consistency criteria, although local quadratic traces remain detectable. The results suggest a distinction between boundary geometry and boundary-layer state. The quadratic exponent appears to represent a robust local geometric feature, whereas layer width and amplitude consistency behave as state-dependent quantities. This work provides a numerical foundation for future two-parameter investigations in (μ, γ)-space and subsequent studies within the Boundary Information Geometry (BIG) program.